Enter num sides : 8 Enter num sides of polygon: 20
Enter num polygons: 10 Enter num polygons: 20
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(3) In the book Liber Abaci, Leonardo of Pisa (better known as Fibonacci) considers pairs of breeding rabbits in an enclosure.
• At the start of month zero there is a single infant pair of rabbits.
• A pair of rabbits matures in 2 months.
• Rabbits do not breed in their first month of life.
• Each mature pair of rabbits produces an infant pair of rabbits on the last day of each month, starting with the second month.
• Rabbits are not mortal.
Leonardo asks: How many pairs will there be one year after this pair begins breeding. For more information about Fibonacci’s problem see: https://tinyurl.com/y5sadcpb
Let F[j] denote the number of pairs in month j. A slight modification of the above problem gives:
F[0] = 0, F[1] = 1,and F[j] = F[j − 1] + F[j − 2], n ≥ 2
(a) Write program FibonacciSeq.py that prompts the user for a positive integer n and then computes and prints out the Fibonacci sequence up to F[n]. You program should print the sequence with 5 Fibonacci numbers per line (except in the last line). The Fibonacci numbers for the range above are at most 4 digits. Use print(’{:5d}’.format(F[j]), end="") to print values with widths of 5 digits. This will give a reasonable display (we will examine formatted output in the next lab). What is the answer to Leonardo’s question?
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You will need to refer to:
https://docs.python.org/3/tutorial/datastructures.html for list methods.
(b) Make your program print compute the ratio: for 2 ≤ j ≤ 20.
The limiting value of is known as the Golden Ratio. It appears in
unexpected places
(see https://www.mathsisfun.com/numbers/golden-ratio.html scroll down to ”FIbonacci Sequence”).
(c) Sketch the Fibonacci Spiral. The Fibonacci spiral is made up of quarter circles (i.e. arc of a circle subtended by a 90o angle) passing through the diagonally opposite vertices of squares that have sides in the Fibonacci sequence. Use the functions you wrote in Lab 5 to draw the arc. The figure on the left, with the squares, is to illustrate the drawing. The figure on the right is what your curve should look like ( the first arc is drawn with the turtle facing East). To illustrate, each quarter circle arc is a different colour. The side lengths are scaled by a factor of 5 (i.e. a square of side length ` will be 5 · ` in the drawing. Your function goldenSpiral.py, takes a turtle as a parameter and have a default parameter n = 10 for the number of arcs that make up your spiral.
Ex. of Spiral with squares drawn in Golden Spiral with n=10 & scale = 5
